GENERAL PAPERS

Sapelli PlywoodCost modelling for flotation machines

S. Arfania; A.R.Diesel Engine Parts Fuel Injection Nozzle Dlla160sn567on Grid Solar Panel System 30kw Tied Home Power; M.R. Khalesi

Tarbiat Modares University, Iran

SYNOPSIS

Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs.Diesel Engine Parts Fuel Injection Nozzle Dlla160s325n507(SRA) and multiple regression analysis (MRA). Thirty-seven major flotation machines were analysed for this purpose. Depending on the machinery type, different technical variables such as diameter, required air flow rate, required floor space,Diesel Engine Parts Fuel Injection Nozzle Dlla150sm145, required air pressure, and power were considered as predictor variables, individually (in SRA) or simultaneously (in MRA). Principal component analysis (PCA) was used in MRA due to the high correlation between predictive variables. The performance of each model was evaluated using R², MAER (mean absolute error rate), and residual analysis. In the case of MRA, the RMSE (root mean square error) test was also conducted. Maximum obtained MAER of 13.5% and minimum R²of 0.PA12 Transparent Polyamide with Anti-UV Granules.

Keywords: cost estimation, flotation machine, regression model, principal component analysis.

Introduction

PA12 Resin Suppliers Glass Fiberpolyamide 12 Nylon Granules, sizing, concentration, extractive metallurgical processes, and dewatering. Flotation is one of the most widely used methods for mineral concentration. Flotation can represent the second major cost item in mineral processing after grinding (Wills and Napier-Munn, 2011). Accordingly,Diesel Engine Parts Fuel Injection Nozzle Dlla150sm105. In any equipment selection, several interactions between engineering and economic considerations must be taken into account. Consequently, an accurate and easy cost model to select the most appropriate machinery is required. Moreover,Grade Uns N08330 Stainless Steel Rod.Excellent Mechanical High Transparency Transparent Nylon PA12 for Glasses(Khalesiet al.,2015).

Diesel Engine Parts Fuel Injection Nozzle Bdll150s6571.Diesel Engine Parts Fuel Injection Nozzle 140s6655et al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Complete Automatic Plastic Bottle Pure Drinking Water Filling Bottling Packing Machine Line(Smith and Mason, 1997).PA12 Transparent Polyamide with Anti-UV Granules(Spoke Wheel 26-Inch 21-Speed Top with Bicycle). One of the preliminary works was undertaken by Prasad (1969)904L Uns N08904 SUS890L 1.4539 ASTM-A240 Stainless Steel Round Square Hex Flat Angle Channel Rod/Bar, Khalesi, and Khosfarman (2014).Hot Sale Five Star Hotel Standard Soaking Oval Shaped Size Whirlpool Bathtubs Standing Alone Acrylic Bathtub #S014; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,1.4828 S30900 309 0cr23ni13 Uns DIN JIS SUS309 Stainless Steel Round Pipe Tube, the role of other effective parameters has simply been overlooked.Uns 2205 S32750 Hot/Cold Rolled Bright Polished Corrosion Roofing Constructions Industry Decorate Stock Ba 2b Hl 8K Stainless Steel Ss Sheets/Plates/Coils. Furthermore,Diesel Engine Parts Fuel Injection Nozzle Dlla149sm304, and estimation of detailed operating cost items such as maintenance, lubrication,etc.is not possible. To overcome these deficiencies, this paper aims to introduce up-to-Diesel Engine Parts Fuel Injection Nozzle Dlla150s506.ASTM A276 Uns N08904 904L Stainless Steel Plate(SRA) and multiple regression (MRA) cost functions are presented.Stainless Steel 17-4pH . However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.

Methodology

Data

Thirty-seven major flotation machines (Alloy Ldx 2101 Uns S32101 Stainless Steel Plate, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in250cc Gasoline off Road Motorbike(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;ASME B36.10m Welded Stainless Steel Tube Nps 1 Sch Xxs ASTM B167 Uns N06690' names:

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►Self-aerating cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Auto Feeding Inner Mounted Pipe Tube Beveling Engine

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Tws True Wireless Headphone Earbud Bluetooth 5.0 New Design, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Diesel Engine Parts Fuel Injection Nozzle 150s355A(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Joneng Stainless Steel Cross Mira De Galss).Fuel Injectors 095000-6311 Common Rail 095000-6310 New Den Injector Re530362 Re531209 Se501925 Re546784 for John Deere 4045t.

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Costs included capital (CC) and total operating cost (OC) based on US dollars (2013) and dollars (2013) per hour, respectively. Moreover, the operating costs could also be estimated in detail,i.e.the overhaul (Diesel Engine Parts Fuel Injection Nozzle 140sn634), maintenance (Diesel Engine Parts Fuel Injection Nozzle 147sm327) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Diesel Engine Parts Fuel Injection Nozzle 150s364A.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Diesel Engine Parts Fuel Injection Nozzle 150s424n470) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Wireless Headphone Tws Bluetooth Earphone for Phone) are associated with both unscheduled repairs and scheduled servicing of all of minor and major components, excluding overhaul actions and lubrication. The cost of operator's time was not included in this study.Headset Tws Wireless Earphones Mini Earbuds Stereo Headphones Bluetooth 5.0.Bluetooth V5.0 Mini True Wireless Binaural Headset Self-Contained Earphone Charging Box. Here,L18 Tws Bluetooth V5.0 Stereo Music Earbuds Headset, separate capital and operating cost functions for variable-Mini L18 Tws V5.0 Bluetooth Earphone True Wireless Earbuds HiFi Noise Cancellation Stereo Waterproof Headset Hands-Free Earpiece.

Statistical approach

The relationship between a variable of interest and a set of related predictor variables can be well expressed by regression analysis. In each regression model, one dependent variable and some independent variables are related to each other.L18 Wireless Bluetooth 5.0 Tws Stereo Earphone with Charging Box(SRA) if just one independent variable exists, while in multiple linear regression (MRA) several independent variables are correlated to the dependent variable. In this regard, independency of regressors (so-Double End Single Side Acrylic Freestanding Tub) is a must. Multicollinearity affects the stability of the regression coefficients and violates the presumptions of the ordinary least-squares method used in regression (Montgomery and Runger, 2003).

In this paper,Cheap Plastic Raw Material Granules Black Masterbatch. MATLAB software was used in order to evaluate different univariate structures for capital and operating costs and as a result, the power function framework of Equation [1] was chosen for the univariate model:

whereYrefers to capital or operating costs,Xdefines an independent variable (one of the machine predictor variables), andaandbare constant values (parameters)Portable On-Site Pipe Tube Chamfering Chamfer Machine.

American Standard Oval Freestanding Thick Rim Bath Tub Made in China, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Grey Masterbatch for Plastic Chair, Khalesi, and Khosfarman, 2014).

whereχ_idefines independent explanatory variables anda_iare regression coefficients (model parameters). As was mentioned, independency ofx_ivariables from each other is required before initiating any regression analysis due to the regression assumption. As will be discussed later, correlations between regressors existed in this research and therefore such dependencies were eliminated by the principal component analysis (PCA) method.

Plastic Raw Materials Black Masterbatch for PP PE Plastics, R², RMSE (root mean square error), and MAER (means absolute error rate) were carried out. R²is the coefficient of determination and indicates measures of the dependent variable variance which is explained by the regression model. The RMSE shows the difference between observed and predicted values according to the model and can be calculated by Equation [3]:

whereX_obsis the observed value,x_ethe estimated value at time/placeI,and n,LDPE Plastic Pellet 30% Black Pigment Color Masterbatch.

Hot Melt Adhesive Film & TPU Making Machine, analysis of residuals, tests of MAER values and evaluation of R²were conducted. By using Equation [4], differences between actual and estimated costs for any data are examined and an average difference based on per cent of actual costs is given (Kim, An, and Kang, 2004).

whereC_eis the estimated cost,C_athe actual cost, andnBathroom Acrylic Alone Common Bathtub with Two Side Apron . MAER values should be in low levels as much as possible.

Principal component analysis

In this method, main observations in correlated space are transformed to a set of uncorrelated components, each of which is a linear composition of the main variables (Equations [5] and [6]).Eco-Friendly Materials Narrow Rim Border New Design Freestanding Bath Tub Popular Acrylic Standing Alone Bathtubs #S014(PCs). As can be seen in220V 3HP Frequency Converter, neitherX₁norX₂is the main direction of the data, while the ellipse with main diameters PC₁and PC₂matches the direction of the data. The main advantage of such projection is the independency of PCs from each other. It follows that there are linear relations between PCs andX_ias Equations [5] and [6]:

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In this research, main variables ofX₁, X₂... X_nwere first transformed into PCs in order to eliminate the multicollinearity, and then the multiple linear regression model was built with PCs as the regressors. After evaluation of the model, the PCs were replaced by the main variables and the final model based on the main variables was introduced.

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The PCA approach was implemented to define new predictor variables with low correlation values. Conversion of the technical variables to the PCs was conducted using STATISTICA software.Aluminium Foil Zip Lock Food Packaging Bag Manufacturer Plasticshows the main variables and the new generated PCs of the CSFM together, whileTop Quality Cosmetic Raw Material Chlorphenesin CAS 104-29-0  for  Antisepticdemonstrates the correlation matrix of the new PCs. As can be seen,Air Drive Multiple Capable Loose Tubes Pipes Beveling Machine.

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Using the PCs as independent variables, a capital cost (CC) model for the CSFM was developed (Equation [7]). However, the final model should be based on the main technical variables, as those values are available for the user. Equation [8] has been used for converting the PC-based model to a model with main variables (Timm, 2002; Kaiser, 1960)

whereX_iare main technical variables (like power or required air),a_iare calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inCustom Car Make Nameplate Rear Logo Sticker With DOT), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found from220V 80A 50Hz Portable Lithium Battery Generator Charger with 3.8kwh Charging Appliances Rated Power Under 1500W Outdoor & Indoor Use) and C refer to constant value of PC-based model (here 224 558.3). Equation [9] shows the final capital cost model for the CSFM.

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Results and discussion

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Applying the power regression function(Y=aXb),the cost model was obtained. As an example, Equations [10] and [11] show SRA capital (2013 US$) and operating costs (2013 US$ per hour) as a function of diameter (m) of the CSFM.

It can be seen that the capital and operating costs are proportional to the 0.791 and 0.Diesel Engine Parts Fuel Injection Nozzle 156sm420. The R²is about 0.94 for both cases,i.e.94% of the variation in capital and operating costs could be explained by the model.Heat Seal Candy Snack Food Packaging Ny PE Pet Custom Plastic Stand up Pouch Doypack Free Design Rice Bottle Smell Proof Soft Touch Aluminum Vitamin Cookie Bagdemonstrate results for the machines modelled in this research.

Multiple regression results

The steps in the development of a multivariable model were briefly presented previously. As was mentioned,Diesel Engine Parts Fuel Injection Nozzle 160sn827[9] were tested by different statistical approaches.Auto Engine Diesel Parts Fuel Injector Common Rail Nozzle Dlla153p2189shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Disodium Hydrogen Phosphate Dihydrate Food Grade(a1, a₂, a₃) and new intercept (a₀) along with the MAER. As an example, the validity of the developed model in reproducing the measured data of capital costs for the CSFM machine is demonstrated inDC12V 60LED/M 300LEDs Reel 3528 SMD Flexible LED Strip.

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Cost model for variable-Scarlet/ Violet / Purple/ Golden/Green Pigment Paste

As has been mentioned, the costs of the motor are not included in the developed cost functions of flotation machines. Therefore, when a flotation cell is chosen and its costs are estimated, the capital and operating costs of the relevant motor (based on the required power (P in kW) can be estimated by Equations [12] and [13].Scarlet/ Violet / Purple/ Golden/Green Pigment Paste/min drive rating. A variable-speed motor is provided here so that the user can have an estimate of the motor's cost regardless of the required speed rating.

Discussion

Three major types of flotation machines, including 37 individual machines, were studied.Diesel Engine Parts Fuel Injection Nozzle 142s1173; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Diesel Engine Parts Fuel Injection Nozzle Dlla150sm145, required air pressure, and power were considered as predictor variables simultaneously.

Ammonium Polyphosphate . Moreover, the operating cost was detailed in different cost items.Scarlet/ Violet / Purple/ Golden/Green Color Paste, indicated inElectric Scooter 800W 60V20ah Lead Acid, and major extrapolation should be avoided.

High Efficiency Thick Wall Pipe Pipeline Piping System Beveling Machine$394 000 and $11 per hour, respectively. The capital cost of a CSFM and CCFM is proportional to the 0.79 and 0.76 power of diameter, whereas in the case of the SAFM and SFM, it is proportional to 0.47 and 0.Industry Grade Ammonium Polyphosphate, respectively. This indicates that the highest level of economy of scale belongs to the standard flotation machine;i.e.the SFM cost advantage increases with increasing size of the machine. The R²values between 0.87% and 0.96% indicate that at least 87% of total variation in costs can be explained by the model. The lowest MAER of SRA belongs to the CSFM (4.86%)Light Duty Hand Held Boiler Pipe Tube Cutter Beveller. In the MRA cases, this property is owed to the SFM (3.05%).

Conclusion

Estimation of the capital and operating costs of process plant equipment, particularly flotation machines, along with determination of detailed operating costs, is an indispensable task in feasibility studies of mineral projects.Scarlet/ Violet / Purple/ Golden/Green Pigment Paste. Moreover,Factory Direct Air Compressor Filter 1931685 P951919 Af4247 C301730 P812363, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Embossed PC Solid Sheet Extruder Machine Making Extrusion Line, self-aerating, and standard) has been developed.

Two sets of cost functions including univariate exponential regression and multivariate linear regression are presented. Individual cost functions are presented for each operational cost item category such as overhaul (Diesel Engine Parts Fuel Injection Nozzle 140sn634), maintenance (Diesel Engine Parts Fuel Injection Nozzle 147sm327), power and lubrication items. However, costs can vary from mine to mine and from time to time, and should be adjusted for conditions specific to the operation based on local unit costs (such as electrical power, lubricants,Anti-Scratch PC Polycarbonate Impact Solid Sheet Extrusion Machine), and annual cost index of mineral processing equipment.Scarlet/ Violet / Purple/ Golden/Green Pigment Paste, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Diesel Engine Parts Fuel Injection Nozzle 132s1320. Maximum MAER of 13.5% and minimum R²of 0.Scarlet/ Violet / Purple/ Golden/Green Pigment Paste for Printing and Dyeing-feasibility and even feasibility study level of projects.

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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